 CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024

# Computability

The course is not on the list Without time-table
Code Completion Credits Range Language
NIE-VYC Z,ZK 4 2P+2C English
Garant předmětu:
Lecturer:
Tutor:
Supervisor:
Department of Applied Mathematics
Synopsis:

Classical theory of recursive functions and effective computability.

Requirements:

Basic course in logic.

Syllabus of lectures:

1. Introduction. Elementary recursive functions.

2. Primitive recursive functions. Ackermann function.

3. General recursive functions. Universal functions.

4. Partial recursive functions.

5. Turing machines.

6. The power of Turing machines.

7. Universal machine. Halting Problem.

8. The equivalence of Turing machines and recursive functions.

9. Arithmetics: coding the language.

10. Recursive axiomatization.

11. (In)completeness and (un)decidability.

12. Diagonal lemma, Gödel's theorem.

Syllabus of tutorials:

1. Elementary recursive functions.

2. Primitive recursive functions

3. General recursive functions.

4. Partial recursive functions.

5. Turing machines.

6. Programming Turing machines.

7. Programming Turing machines.

8. Programming Turing machines.

9. Gödel coding and decoding.

10. Decidability: examples.

11. Undecidability: examples.

12. Diagonalization.

Study Objective:

The basic formalizations of an „algorithm“ and elementary questions of computability.

Study materials:

1. Church: An unsolvable problem of elementary number theory

2. Church: A note on the Entscheidungsproblem

3. Davis: Computability and unsolvability

4. Enderton: Elements of Recursion Theory

5. Kleene: Introduction to Metamathematics

6. Rogers: Theory of Recursive Functions and Effective Computability

7. Shoenfield: Mathematical Logic

8. Turing: On computable numbers

9. Černý: Výpočty I

Note:
Further information:
No time-table has been prepared for this course
The course is a part of the following study plans:
Data valid to 2023-10-04
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